hw5_sol.pdf

# hw5_sol.pdf - CO 370 Homework assignment 5 Fall 17 Page 1...

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CO 370 - Homework assignment 5 Fall ’17 Page 2 (1) is always feasible and bounded, thus it has an optimal solution, thus by strong duality, we can rewrite (1) as min 16 α s.t 2 α ¯ x 1 4 α ¯ x 2 α ¯ x 3 α ¯ x 4 α 0 25 (2) By a result seen in class, we can thus rewrite (ROB) as the following LP max 2 x 1 + x 2 + 3 x 3 + 5 x 4 s.t. 16 α 25 2 α x 1 4 α x 2 α x 3 α x 4 α 0 x 0 (ROB-LP) (b) (10 points) Consider now that there are five possible scenarios for the set of coefficients ˜ a , each can happen with a probability of 0.2: 1. ˜ a = (1 , 1 , 1 , 9) 2. ˜ a = (1 , 1 , 9 , 1) 3. ˜ a = (5 , 1 , 1 , 1) 4. ˜ a = (1 , 3 , 1 , 1) 5. ˜ a = (1 , 1 , 1 , 1) John decides to write a two-stage stochastic program to decide how much to produce per day (in advance, before knowing ˜ a ). If the decision that John takes exceeds the total available units of the
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• Winter '11
• henry
• Optimization, Approximation algorithm, optimization problem

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